Wash and sterilize 4 (1-pint) jars and closures, stand on a baking sheet, and keep hot in a 250° F. oven until needed.
Simmer mushrooms in brine, covered, 5 minutes, then drain.
Into each hot jar place 1 clove garlic, 1 bay leaf, 1/4 teaspoon each cloves and peppercorns, and 1 chili pequin.
Heat vinegar and oil to boiling in an enamel or stainless-steel saucepan, add mushrooms and simmer, uncovered, 5 minutes.
Remove mushrooms with a slotted spoon and pack into jars, then pour in boiling vinegar mixture, filling to within 1/8" of tops.
Wipe rims and seal.
Cool, check seals, label, and store in a cool, dark, dry place 2-3 weeks before serving.